[cornholio]

A good pseudorandom generator will pass any such test with flying colours, in fact it's a basic requirement. Bu that is no guarantee that, given a certain length of output, an external attacker couldn't sync up and predict all future outputs.

And I don't believe there is a general way to distinguish such a device from an actual random source without looking inside. For example, they could use AES256 output in counter mode on a low entopy chip ID + high entropy backdoor key. Trivial to bruteforce given a few words of output, but you would essentially need to break AES to detect it.